Question

compare the weight of the object on a planet whose mass is twice the mass of earth and radius is 4 times the radius of earth​

Answer 1

Answer:

• Weight of object on the planet (W') is related to the weight of the object on Earth (W) as., W / W' = 1 / 8

Explanation:

Let, The mass of Earth be M

The Radius of the earth be R

Then, Using the formula

• g = GM / R²

[ Where g is acceleration, G is universal gravitational constant, M is mass and R is the radius for a given planet]

So,

On Earth, Acceleration due to gravity g will be,

→ g = GM / R²

Now, For A planet whose mass is twice of the mass of earth and radius is 4 times the radius of the Earth.

Mass of planet will be 2M

and, Radius of the planet will be 4R

So, On this planet, Acceleration due to gravity g' will be,

→ g' = G 2M / (4R)²

→ g' = 2 GM / 16R²

→ g' = (2/16) GM/R²

Hence, we can conclude that

→ g / g' = 2 / 16 = 1 / 8

Now, Since

Weight = mass × acceleration due to gravity

So, For any object of mass m

→ Weight of object at Earth (W) / Weight of object at Planet (W') = ( m g ) / ( m g' )

→ W / W' = g / g' = 1 / 8

→ W / W' = 1 / 8

Therefore,

• Weight of object on the planet (W') is related to the weight of the object on Earth (W) as., W / W' = 1 / 8.